I actually got the harder badge before the medium badge. Haven't got that yet, I think I need a few more upgrades.
I try to collect as many fuel refills as possible on the way up.
I'd love to know how you're supposed to pass a wave when sometimes there are ships outside of the borders of the screen and you don't ever actually see them...
Some of these are actually tricky, and indeed a little random. Such as one of the later levels where the rubble can't hit the building next door. Minute changes in dynamite placement seem to make a big, big difference.
I had a problem in the 'don't think, outsmart' room - I ended up lagging when the spikes came into the room and simply couldn't get up the first jump...